Question

If $y=2^{ax}$ and $\frac{dy}{dx}=\log 256$ at $x=1$, then the value of $a$ is

Answer 1

$y=2^{ax}$
$\Rightarrow$$\frac{dy}{dx}=2^{ax}\cdot \log 2\cdot a$
at $x=1,$
$\frac{dy}{dx}=\log 256=\log 2^8$
$\Rightarrow 2^a\cdot \log 2\cdot a=8\log 2$
$\Rightarrow 2^a\cdot a=8$
$\Rightarrow a=2$